The RaboDirect PRO12 champions have been hugely impressed by the progress made under the former Wales and Cardiff RFC hooker.
Humphreys is under contract until the end of next season but the Ospreys are keen to tie down their forward coach's long-term future.
"He has been superb," Andrew Hore, the region's chief operations officer told the South Wales Evening Post.
"We will sit down with Jonathan to discuss his ambitions because how he sees his career developing is vitally important as well.
"But I would like him to stay at the Ospreys.
"He still has a while on his contract but in time we will meet with him and explore the possibility of extending it."
The Ospreys pack laid the foundations to last season's league triumph, with the set-piece a major feature, and weapon, of the region's play.
Humphreys has been attributed to the forward dominance and has also received credit for developing the young talent within the region.
"He has had terrific flak in the past but he has developed into a world-class forwards coach," said Hore.
"All those front-row forwards haven't come through by chance. Humph has helped to nurture them and develop their games. He is from this area, too.
"The other week I went to the reopening of the boxing gym in Pyle that he helped raise money to restore.
"People associate him with the Blues because he played a lot of rugby for Cardiff, but he is from the Ospreys area and totally committed to the cause."